I've always taken it to be nonsense syllables, like "With a hey nonny no" in Shakespeare's time or "Sh-boom" and "Sha-la-la-la"" in Doo-Wop or scat singing in jazz.
I never really gave it any thought before. I think it is a nonsense phrase but now wonder where it came from. It pops up in a fair few songs,e.g., Bing Crosby's An Irish Lullaby and Courtin' in the Kitchen (trad.).